Your productivity as a researcher can be measured by your total number of articles, and the impact of your research can be measured by the total number of times your articles have been cited. The h-index (AKA Hirsch index) is a combined measure of both productivity and impact. An index of h means that your h most highly-cited articles have at least h citations each.
The h-index is more informative than total number of articles (which ignores how well those articles have been received by other researchers) or total number of citations (which can be inordinately influenced by a small number of highly-cited articles and therefore not an accurate reflection of productivity).
One caveat about the h-index is that it correlates with the length of a researcher's career (i.e., researchers who have been publishing for longer tend to have higher h-indices). It can also be inflated by self-citation. In addition, the h-index ignores the order of authorship, which is very important in some disciplines. Additionally, because different disciplines have different publishing practices, the h-index should not be used to compare researchers across different disciplines. Average impact scores vary widely from discipline to discipline.
***Web of Science (Emory subscription): Search for an author, then click Create Citation Analysis to calculate h-index and see trends in impact across time.
***Scopus (Emory subscription): Search for an author, then select the correct author, select all articles of interest, then click View Citation Overview to calculate number of citations and h-index (full citation information available for articles published in 1996 or after).
Google Scholar: To calculate your h-index and see trends in your impact across time, create a public or private profile. Unlike other databases, Google Scholar provides citation information not only for journal articles but also for conference papers and books.
Publish or Perish: Download this free software, which uses information from Google Scholar to calculate h-index and several h-index alternatives. A companion user's guide, The Publish or Perish Book, is available in the Emory book stacks.
Scholarometer: Install this browser (Firefox or Chrome) extension and search for an author to receive a list of articles, number of citations, h-index, and h-index alternatives based on information from Google Scholar.
Google Scholar Universal Gadget: Search for an author, and this gadget uses information from Google Scholar to calculate number of citations and h-index.
Microsoft Academic Search: Search for an author to calculate h-index and see trends in impact across time.
h-index Prediction Tool: Predict what your h-index will be in the future.
NOTE: As these tools use different ways of searching for articles and citations, they tend to provide differing results.